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AlgebraQuestion and Answers: Page 299

Question Number 71633 Answers: 1 Comments: 0

let a,b,c ∈IR_+ show that (a+b)(a+c)≥2(√(abc(a+b+c)))

$$\mathrm{let}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\in\mathrm{IR}_{+} \\ $$$$\mathrm{show}\:\mathrm{that}\:\left(\mathrm{a}+\mathrm{b}\right)\left(\mathrm{a}+\mathrm{c}\right)\geqslant\mathrm{2}\sqrt{\mathrm{abc}\left(\mathrm{a}+\mathrm{b}+\mathrm{c}\right)} \\ $$$$ \\ $$

Question Number 71534 Answers: 2 Comments: 0

a number consists of digits 1 and 2. the sum of its digits is 2018. if the number is multiplied with 5, the sum of the digits will be 10000. find how many digits this number has.

$${a}\:{number}\:{consists}\:{of}\:{digits}\:\mathrm{1}\:{and}\:\mathrm{2}. \\ $$$${the}\:{sum}\:{of}\:{its}\:{digits}\:{is}\:\mathrm{2018}. \\ $$$${if}\:{the}\:{number}\:{is}\:{multiplied}\:{with}\:\mathrm{5},\: \\ $$$${the}\:{sum}\:{of}\:{the}\:{digits}\:{will}\:{be}\:\mathrm{10000}. \\ $$$${find}\:{how}\:{many}\:{digits}\:{this}\:{number} \\ $$$${has}. \\ $$

Question Number 71533 Answers: 1 Comments: 0

Three interior angles of a nonagon are equal and the sum of the other six is 1050° Find the size of one of the equal angles.

$$\mathrm{Three}\:\mathrm{interior}\:\mathrm{angles}\:\mathrm{of}\:\mathrm{a}\:\mathrm{nonagon}\:\mathrm{are} \\ $$$$\mathrm{equal}\:\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{other}\:\mathrm{six}\:\mathrm{is}\:\mathrm{1050}° \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{size}\:\mathrm{of}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equal}\:\mathrm{angles}. \\ $$

Question Number 71518 Answers: 1 Comments: 8

Express (√(28)) as continued fraction

$$\mathrm{Express}\:\:\sqrt{\mathrm{28}}\:\:\mathrm{as}\:\mathrm{continued}\:\mathrm{fraction} \\ $$

Question Number 71448 Answers: 0 Comments: 1

find the domain f(x)=(1/(sin(sin(x))))

$${find}\:{the}\:{domain} \\ $$$$ \\ $$$${f}\left({x}\right)=\frac{\mathrm{1}}{{sin}\left({sin}\left({x}\right)\right)} \\ $$

Question Number 71406 Answers: 0 Comments: 6

Hello Solve (x^2 )^(1/3) −3((x(x−1)))^(1/3) +2((x−1))^(1/3) =0

$$\mathrm{Hello}\: \\ $$$$\mathrm{Solve}\:\sqrt[{\mathrm{3}}]{\mathrm{x}^{\mathrm{2}} }−\mathrm{3}\sqrt[{\mathrm{3}}]{\mathrm{x}\left(\mathrm{x}−\mathrm{1}\right)}+\mathrm{2}\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{1}}=\mathrm{0} \\ $$

Question Number 71282 Answers: 4 Comments: 0

solve x(y+z)=27 y(z+x)=32 z(x+y)=35

$${solve} \\ $$$${x}\left({y}+{z}\right)=\mathrm{27} \\ $$$${y}\left({z}+{x}\right)=\mathrm{32} \\ $$$${z}\left({x}+{y}\right)=\mathrm{35} \\ $$

Question Number 71242 Answers: 3 Comments: 0

Given: (a/b) + (c/d) = (b/a) + (d/c) Show that, (a^2 /b^2 ) − (c^2 /d^2 ) = (b^2 /a^2 ) − (d^2 /c^2 )

$$\mathrm{Given}:\:\:\:\frac{\mathrm{a}}{\mathrm{b}}\:+\:\frac{\mathrm{c}}{\mathrm{d}}\:\:=\:\:\frac{\mathrm{b}}{\mathrm{a}}\:+\:\frac{\mathrm{d}}{\mathrm{c}} \\ $$$$\mathrm{Show}\:\mathrm{that},\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{a}^{\mathrm{2}} }{\mathrm{b}^{\mathrm{2}} }\:−\:\frac{\mathrm{c}^{\mathrm{2}} }{\mathrm{d}^{\mathrm{2}} }\:\:=\:\:\frac{\mathrm{b}^{\mathrm{2}} }{\mathrm{a}^{\mathrm{2}} }\:−\:\frac{\mathrm{d}^{\mathrm{2}} }{\mathrm{c}^{\mathrm{2}} } \\ $$

Question Number 71196 Answers: 1 Comments: 0

the curve y = f(x), when f(x) is a quadratic expression has a maximum value point at (1,4). The curve touches the line 6x + y = 13. Find the value of x for which y = 8

$${the}\:{curve}\:{y}\:=\:{f}\left({x}\right),\:{when}\:{f}\left({x}\right)\:{is}\:{a}\:{quadratic}\:{expression}\:{has}\: \\ $$$${a}\:{maximum}\:{value}\:{point}\:{at}\:\left(\mathrm{1},\mathrm{4}\right).\:{The}\:{curve}\:{touches}\:{the}\:{line} \\ $$$$\mathrm{6}{x}\:+\:{y}\:=\:\mathrm{13}.\:{Find}\:{the}\:{value}\:{of}\:{x}\:{for}\:{which}\:{y}\:=\:\mathrm{8} \\ $$

Question Number 71172 Answers: 0 Comments: 2

find fhe range f(x)=(4/(1+(√x)))

$${find}\:{fhe}\:{range} \\ $$$$ \\ $$$${f}\left({x}\right)=\frac{\mathrm{4}}{\mathrm{1}+\sqrt{{x}}} \\ $$

Question Number 71147 Answers: 2 Comments: 1